AA v KK

[KenProspero]

In my last 4500 hands, I've had KK and been up against AA 5 times. Back of the envelope, I figure I should have KK and see AA should happen about once in 5000 hands. (In a full table, I'll get KK once in 221 hands -- One of my 9 opps will have AA about 1 time in 23).

First: How close is this guestimate.

Second: What are the chances of this occurring 5 times in 4500 hands.

I suspect the odds aren't astronomical, but can't do the math. Thanks.

[Tom1975]

Assuming your 1 time in 23 figure is accurate for the chance one of your oppenents has KK when you have AA, this should happen once in 221*23=5083 hands. To figure the chances of a 1 in 5083 event occuring 5 times in 4500 trials you can use the binomial distribution to get your answer. This a handy built-in function in excel:

BINOMDIST(5,4500,(1/5083),FALSE)=.001867

[AaronBrown]

Your 1/221 is exact.

Given that you have KK, one or two of 9 other players will have AA 2,529 times out of 57,575.

Therefore, you expect this to happen once every 5,031 hands.

It will happen five or more times out of 4,500 hands 0.2% of the time or one time in 439. So it's unlikely, but not extraordinarily so.

[ohnonotthat]

* Lee Jones' friend's way of stating that regardless of how unlikely an event's occurence may be sooner or later it must occur - provided it is indeed unlikely and NOT impossible.

I'm wondering if the typical person has a cut-off point below which "he" yawns and says s--t happens and above which he sits up and takes notice.

I've seen A-A dealt three times in a row to the same player many times (though I myself have not yet been blessed with this trifecta).

I was once dealt 7-7 three times in a row, played it all three times, flopped sets all three times and in the "you'll never believe it" category WON all three hands.

Oh, yeah - I also RAISED preflop all three times . . . BB, SB and button

- Amazingly loose (live) 10-20 game

I probably should not have raised from either blind; in spite of having 5+ callers this was likely not a good move since these psychos were planning to stay till the end whether I chummed the waters or not. (Using this same reasoning it's debatable whether even the button raise was warranted tho in that hand all seven opponents were in).

Even if we take it as a given that I would never fold this hand vs this group (not far from true) calculating the chances of this event occuring is extremely cumbersome as it's very difficult to quantify my chances of winning if I flop a set - not to mention my chances of winning if I don't.

Still, just getting the same pair three times in a row and flopping a set each time is 1: 221 x [approx] 8.5 cubed, OR better than SIX BILLION TO ONE.

(Aaron will spot the mythical error in this method of computing this figure but what is a billion or so between friends [img]/images/graemlins/smile.gif[/img] )

If we lower the requirements to ANY pair being received three times in a row and flopping a set each time we are still talking Ripley's material.

I cannot quote the source (and am likely to muddle the finer details) but a respected mathmatician once calculated that a chimpanzee who working 40 hours/week at a typewriter would at somepoint within ~400 years produce a very close facsimile to Hamlet.

Then there's this evolution thing [img]/images/graemlins/wink.gif[/img].

This is getting perilously close to a branch of math at which I am less than competent (i.e., which is mathmatically more likely, creation or evolution - which among other things involves a form of Bayes' Theorum) while moving farther and farther from anything of a practical use but it's difficult not to find the topic fascinating.

Oh, yeah - it happened on July 7th (7-7).

- I have witnesses.

[KenProspero]

[ QUOTE ]
Given that you have KK, one or two of 9 other players will have AA 2,529 times out of 57,575.

[/ QUOTE ]

So, my 'back of the envelop' 1 in 23 was pretty close -- good to know I'm not totally off in math.

[ QUOTE ]
It will happen five or more times out of 4,500 hands 0.2% of the time or one time in 439. So it's unlikely, but not extraordinarily so.

[/ QUOTE ]

Thanks!! As I posted above, I didn't think the odds were astronomical, so it's sorta what I expected.